Does a replacement Yaw rate sensor need to be programmed?

Yes the offset needs to be reset. The sensor is built with some tolerance in the component and that means it could be a degree off from the old one. As such you need to do a steering angle relearn to let the modules know the full range of travel and where the "zero" point is.
You need the factory equivalent scan tool to do it, once replaced you have to go into the steering sensor and follow the tools directions as you do the reset.

Unless you have a capable scan tool that can access it and put it into program mode so it can do the relearn a shop with the correct tool will be needed. Normally it's done on an alignment table so that you can be sure the tires are straight ahead because the tire should be within 1 degree of straight and then you follow the instructions.